Question

The length of salmon going into a particular river for spawning can be assumed to be normally distributed with the expected length µ = 90 cm and standard deviation σ = 10 cm. The lengths of different salmon are independent.

a) Calculate the probability that a salmon is over 100 cm.
Find the length a which is such that only 1% of the salmon is longer than a cm.
Salmon fishermen in this river have a seasonal quota of 5 salmon. Hanna is an avid salmon fisherman and fisherman until she has filled the seasonal quota. Calculate the probability that the average length of the 5 salmon is over 100 cm.
In a larger watercourse there are two salmon strains, strain A and strain B. For strain A the expected length is µA = 90 and the standard deviation σA = 10, while for strain B is µB = 96 and σB = 8. The lengths are as before independent and normally distributed. .
It is further known that 70% of the salmon in the watercourse is from strain A, while 30% is from strain B.

b) Calculate the probability that a salmon from the watercourse is over 100 cm.
Calculate the probability that a salmon from strain A is longer than a salmon from strain B.

Answer 1